Nonexponential Relaxation of Magnetization at the Resonant Tunneling Point under a Fluctuating Random Noise

At resonant tunneling points of nanoscale molecular magnets, a fluctuating random field causes successive Landau-Zener Stückelberg transitions. We have studied dynamics of magnetization by a Langevin type Schrödinger equation and found that the successive transitions result in a stretched exponential decay with square-root time when the fluctuation of the field is regarded as an random walk, i.e., the Wiener process. When the fluctuation is bounded by a restoring force, i.e., the Ornstein Uhlenbeck process, the relaxation obeys the exponential decay at the late stage, while it shows the stretched exponential decay at the early stage. The scaling relations of the relaxation functions at both stages are also studied as functions of the parameters: the strength of the fluctuation, the restoring force, and the energy gap of the system at the resonant point. Roles of the observed nonexponential decay are also discussed in various kinds of square-root time behavior found in experiments.